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Residual entropy scaling (RES) of thermal conductivity was applied to pure refrigerants, including natural and halogenated refrigerants, and their mixtures. The reference equations of state and the mixture models implemented in the REFPROP software package were adopted to calculate the residual entropy, and the critical enhancement of thermal conductivity was taken into account with the RES approach for the first time. Experimental data of 39 pure fluids with more than 38,000 data points and of 31 mixtures with more than 7600 points were collected and analyzed. More than 95.4% of the data (within two standard deviations of the mean) of pure fluids collapse into a global dimensionless residual thermal conductivity versus scaled dimensionless residual entropy curve within 11.1% and those of mixtures are within 8.3%. This smooth, monotonically increasing curve was correlated with a polynomial function containing only four fitted parameters and one fluid-specific scaling factor. Each pure fluid has its individual scaling factor, and a simple mole-fraction-weighted mixing rule was applied for mixtures. The correlation function provides a reliable thermal conductivity prediction of pure fluids and, without any additional parameters, of mixtures. The proposed model yields a similar level of statistical agreement with the experimental data as the extended corresponding states model, which is the current state-of-the-art and has as many as four more parameters for each pair of components.